Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation

• Numerical solution of the fractional order diffusion equation is given.
• The proposed method is based on shifted Chebyshev polynomials of the second kind.
• Numerical examples are performed to show the reliability of the proposed method.

In this paper, an efficient numerical method for solving space fractional order diffusion equation is presented. The numerical approach is based on shifted Chebyshev polynomials of the second kind where the fractional derivatives are expressed in terms of Caputo type. Space fractional order diffusion equation is reduced to a system of ordinary differential equations using the properties of shifted Chebyshev polynomials of the second kind together with Chebyshev collocation method. The finite difference method is used to solve this system of equations. Several numerical examples are provided to confirm the reliability and effectiveness of the proposed method.